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Article

# Radially Symmetric Solution for Fractional Laplacian Systems with Different Negative Powers

1
School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China
2
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3
School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, China
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2022, 6(7), 352; https://doi.org/10.3390/fractalfract6070352
Received: 26 May 2022 / Revised: 15 June 2022 / Accepted: 16 June 2022 / Published: 23 June 2022
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)
By developing the direct method of moving planes, we study the radial symmetry of nonnegative solutions for a fractional Laplacian system with different negative powers: ${\left(-\Delta \right)}^{\frac{\alpha }{2}}u\left(x\right)+{u}^{-\gamma }\left(x\right)+{v}^{-q}\left(x\right)=0,x\in {R}^{N},$ ${\left(-\Delta \right)}^{\frac{\beta }{2}}v\left(x\right)+{v}^{-\sigma }\left(x\right)+{u}^{-p}\left(x\right)=0,x\in {R}^{N},$ $u\left(x\right)\gtrsim {|x|}^{a},v\left(x\right)\gtrsim {|x|}^{b}\mathrm{as}\phantom{\rule{3.33333pt}{0ex}}|x|\to \infty ,$ where $\alpha ,\beta \in \left(0,2\right)$, and $a,b>0$ are constants. We study the decay at infinity and narrow region principle for the fractional Laplacian system with different negative powers. The same results hold for nonlinear Hénon-type fractional Laplacian systems with different negative powers. View Full-Text
MDPI and ACS Style

Xu, H.; Ahmad, B.; Wang, G.; Zhang, L. Radially Symmetric Solution for Fractional Laplacian Systems with Different Negative Powers. Fractal Fract. 2022, 6, 352. https://doi.org/10.3390/fractalfract6070352

AMA Style

Xu H, Ahmad B, Wang G, Zhang L. Radially Symmetric Solution for Fractional Laplacian Systems with Different Negative Powers. Fractal and Fractional. 2022; 6(7):352. https://doi.org/10.3390/fractalfract6070352

Chicago/Turabian Style

Xu, Haiyong, Bashir Ahmad, Guotao Wang, and Lihong Zhang. 2022. "Radially Symmetric Solution for Fractional Laplacian Systems with Different Negative Powers" Fractal and Fractional 6, no. 7: 352. https://doi.org/10.3390/fractalfract6070352

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